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Extra resources for Nonlinear Theory of Electroelastic and Magnetoelastic Interactions

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0 and then dividing by ıs and letting ıs ! e. t E D 0. 167)1 follows. Now consider a cylinder (or ‘pill box’) of infinitesimal height ıh and crosssectional area ıS D nıS straddling the surface S , as depicted in Fig. 6. 170) V where ˙ is the bounding surface of the cylinder. Since ıh is infinitesimal and the flux of D across the lateral surface of the cylinder becomes negligible as ıh ! 0, the only contributions to the surface integral come from the top and bottom surfaces of the cylinder. 170) is the total free charge in V , which consists of the surface charge f ıS .

76) Now consider a circuit C of finite dimensions carrying current I , as depicted in Fig. 3. Let S be any regular surface that is bounded by C . Imagine that a fine network of curves is constructed on S such that each mesh is infinitesimal, 26 2 Electromagnetic Theory m = IdS S C Γ Fig. 3 An open surface S bounded by a closed circuit C carrying current I . On S is shown a network of curves made up of small current loops with current I corresponding to magnetic dipoles with magnetic moment m D I dS, where dS is the directed area element on S related to the direction of the current by the right-hand screw rule.

X0 / within a volume V , vanishing outside V . 148) has again been used. 158) where the skew-symmetry of M has been used. 63) shows that, for a distribution of dipoles, curl M behaves like a current density and therefore has the interpretation 42 2 Electromagnetic Theory indicated above. 89) for J D Jb . 162) which shows that only the free electric current density Jf remains in Maxwell’s equation. The term @D=@t , the time derivative of the electric displacement, plays a role similar to a current density and is known as the displacement current.